Monty Hall Problem

• http://www.youtube.com/watch?v=P9WFKmLK0dc

Monty Hall Problem

• http://www.youtube.com/watch?v=P9WFKmLK0dc

• Lesson: Can’t always trust your first guess?

Induction

Guess the next number in the following sequences.• 1, 4, 7,…• 1, 4, 9, 16,…

Induction

• Inductive reasoning is the process of reaching a conclusion by examining specific examples.

Pizza! Pizza!

• What is the maximum number of pieces of pizza you can get from 1 cut? 2 cuts? 3 cuts? How about the 5th 6th 7th cuts?

Consider the following expression.

Is this true for every choice for x?

True or not?

If the product of two natural numbers is even, then both of the numbers are even numbers

Balance Puzzle

• The goal is determine the number value or weight of each shape.

• The right and left sides of each horizontal beam must balance.

• Each shape has a unique and consistent weight which is 1 or 2 digit whole number.

• A piece hanging directly below the fulcrum does not affect the balance.

• The size of a piece has no relation to its weight.

Let us reason

We used deductive reasoning to solve the Balance puzzle (Maybe?).

Deductive reasoning is reaching a conclusion by applying general assumptions, procedures, or principles.

Shoes size predicts your age this year!

Write down your shoe size,Multiply it by 50,Add 50,Multiply your answer by 20,Add 1013 to it,Subtract the year you were born from it.Then the first 2 digit will be your shoe size and the last 2 digit will be your age.

Logic Puzzle

Each of four neighbors, Sean, Maria, Sarah and Brian, has a different job (editor, banker, chef, dentists). Determine the job of each neighbor1. Maria gets home from work after the banker but

before the dentist.2. Sarah, who is the last to get home from work, is

not the editor3. The dentist and Sarah leave for work at the same

time.4. The banker lives next door to brian.

Harder Logic Puzzle

The People of Playland only tell the truth on Sunday, Tuesday, and Thursday. Which day of the week is it if the Playlander says “I told the truth yesterday”.

1.1 homework

• 1-15 odd, 25-43 odd, 48.

1.2 Patterns

Consider the sequence

5, 14, 27, 44, 65,….5 = 1st term = 14 = 2nd term = 27 = 3rd term = 44 = 4th term =

sequences

2, 5, 8, 11, 14,… what’s the pattern?

5, 14, 27, 44, 65,… what’s the pattern?

4, 14, 30, 52, 80,….

nth Formula

Come up with the nth formula

nth Formula

• I still haven’t figured this one out!

nth Formula

Consider for

Fibonacci

• Vi Hart

Fibonacci Numbers

True or Not! (get to leave when finished!)

• If is even, then is an odd number.

• for

• Homework 1.2 1-17 odd, 20, 25